Abstract. The numerical implementation of an ocean model based on the incompressible Navier Stokes equations which is designed for studies of the ocean circulation on horizontal scales less than the depth of the ocean right up to global scale is described. A "pressure correction" method is used which is solved as a Poisson equation for the pressure field with Neumann boundary conditions in a geometry as complicated as that of the ocean basins. A major objective of the study is to make this inversion, and hence nonhydrostatic ocean modeling, efficient on parallel computers. The pressure field is separated into surface, hydrostatic, and nonhydrostatic components. First, as in hydrostatic models, a two-dimensional problem is inverted for the surface pressure which is then made use of in the three-dimensional inversion for the nonhydrostatic pressure. Preconditioned conjugate-gradient iteration is used to invert symmetric elliptic operators in both two and three dimensions. Physically motivated preconditioners are designed which are efficient at reducing computation and minimizing communication between processors. Our method exploits the fact that as the horizontal scale of the motion becomes very much larger than the vertical scale, the motion becomes more and more hydrostatic and the threedimensional Poisson operator becomes increasingly anisotropic and dominated by the vertical axis. Accordingly, a preconditioner is used which, in the hydrostatic limit, is an exact integral of the Poisson operator and so leads to a single algorithm that seamlessly moves from nonhydrostatic to hydrostatic limits. Thus in the hydrostatic limit the model is "fast," competitive with the fastest ocean climate models in use today based on the hydrostatic primitive equations. But as the resolution is increased, the model dynamics asymptote smoothly to the Navier Stokes equations and so can be used to address smallscale processes. A "finite-volume" approach is employed to discretize the model in space in which property fluxes are defined normal to faces that delineate the volumes. The method makes possible a novel treatment of the boundary in which cells abutting the bottom or coast may take on irregular shapes and be "shaved" to fit the boundary. The algorithm can conveniently exploit massively parallel computers and suggests a domain decomposition which allocates vertical columns of ocean to each processing unit. The resulting model, which can handle arbitrarily complex geometry, is efficient and scalable and has been mapped on to massively parallel multiprocessors such as the Connection Machine (CM5) using data-parallel FORTRAN and the Massachusetts Institute of Technology data-flow machine MONSOON using the implicitly parallel language Id. IntroductionDetails of the numerical implementation of a model which has been designed for the study of dynamical processes in the ocean from the convective, through the geostrophic eddy, up to global scale are set out. The "kernel" algorithm solves the incompressible Navier Stokes equations on the...

Abstract. Ocean models based on consistent hydrostatic, quasi-hydrostatic, and nonhydrostatic equation sets are formulated and discussed. The quasi-hydrostatic and nonhydrostatic sets are more accurate than the widely used hydrostatic primitive equations. Quasi-hydrostatic models relax the precise balance between gravity and pressure gradient forces by including in a consistent manner cosine-of-latitude Coriolis terms which are neglected in primitive equation models. Nonhydrostatic models employ the full incompressible Navier Stokes equations; they are required in the study of smallscale phenomena in the ocean which are not in hydrostatic balance. We outline a solution strategy for the Navier Stokes model on the sphere that performs efficiently across the whole range of scales in the ocean, from the convective scale to the global scale, and so leads to a model of great versatility. In the hydrostatic limit the Navier Stokes model involves no more computational effort than those models which assume strict hydrostatic balance on all scales. The strategy is illustrated in simulations of laboratory experiments in rotating convection on scales of a few centimeters, simulations of convective and baroclinic instability of the mixed layer on the 1-to 10-km scale, and simulations of the global circulation of the ocean.

The physical climate formulation and simulation characteristics of two new global coupled carbon–climate Earth System Models, ESM2M and ESM2G, are described. These models demonstrate similar climate fidelity as the Geophysical Fluid Dynamics Laboratory’s previous Climate Model version 2.1 (CM2.1) while incorporating explicit and consistent carbon dynamics. The two models differ exclusively in the physical ocean component; ESM2M uses Modular Ocean Model version 4p1 with vertical pressure layers while ESM2G uses Generalized Ocean Layer Dynamics with a bulk mixed layer and interior isopycnal layers. Differences in the ocean mean state include the thermocline depth being relatively deep in ESM2M and relatively shallow in ESM2G compared to observations. The crucial role of ocean dynamics on climate variability is highlighted in El Niño–Southern Oscillation being overly strong in ESM2M and overly weak in ESM2G relative to observations. Thus, while ESM2G might better represent climate changes relating to total heat content variability given its lack of long-term drift, gyre circulation, and ventilation in the North Pacific, tropical Atlantic, and Indian Oceans, and depth structure in the overturning and abyssal flows, ESM2M might better represent climate changes relating to surface circulation given its superior surface temperature, salinity, and height patterns, tropical Pacific circulation and variability, and Southern Ocean dynamics. The overall assessment is that neither model is fundamentally superior to the other, and that both models achieve sufficient fidelity to allow meaningful climate and earth system modeling applications. This affords the ability to assess the role of ocean configuration on earth system interactions in the context of two state-of-the-art coupled carbon–climate models.

The authors present results for simulated climate and climate change from a newly developed high-resolution global climate model [Geophysical Fluid Dynamics Laboratory Climate Model version 2.5 (GFDL CM2.5)]. The GFDL CM2.5 has an atmospheric resolution of approximately 50 km in the horizontal, with 32 vertical levels. The horizontal resolution in the ocean ranges from 28 km in the tropics to 8 km at high latitudes, with 50 vertical levels. This resolution allows the explicit simulation of some mesoscale eddies in the ocean, particularly at lower latitudes. Analyses are presented based on the output of a 280-yr control simulation; also presented are results based on a 140-yr simulation in which atmospheric CO2 increases at 1% yr−1 until doubling after 70 yr. Results are compared to GFDL CM2.1, which has somewhat similar physics but a coarser resolution. The simulated climate in CM2.5 shows marked improvement over many regions, especially the tropics, including a reduction in the double ITCZ and an improved simulation of ENSO. Regional precipitation features are much improved. The Indian monsoon and Amazonian rainfall are also substantially more realistic in CM2.5. The response of CM2.5 to a doubling of atmospheric CO2 has many features in common with CM2.1, with some notable differences. For example, rainfall changes over the Mediterranean appear to be tightly linked to topography in CM2.5, in contrast to CM2.1 where the response is more spatially homogeneous. In addition, in CM2.5 the near-surface ocean warms substantially in the high latitudes of the Southern Ocean, in contrast to simulations using CM2.1.

Height coordinate ocean models commonly represent topography as a ''staircase'' of discontinuous steps that are fitted to the model grid. Here the ramifications of an alternative approach are studied in which ''shaved cells'' are used to represent irregular topography. The problem is formulated using the finite-volume method and care is taken to ensure that the discrete forms have appropriate conservation properties. Two representations of topography, ''partial step'' and ''piecewise linear,'' are considered and compared with the staircase approach in some standard problems such as the topographic ␤ effect and flow over a Gaussian bump. It is shown that shaved cells are clearly more accurate than the conventional staircase representation. The use of partial steps, although not as accurate as the piecewise linear approach, is seen to be superior to the staircase approach. Moreover, partial steps can be readily implemented in existing height coordinate models.

The authors describe carbon system formulation and simulation characteristics of two new global coupled carbon-climate Earth System Models (ESM), ESM2M and ESM2G. These models demonstrate good climate fidelity as described in part I of this study while incorporating explicit and consistent carbon dynamics. The two models differ almost exclusively in the physical ocean component; ESM2M uses the Modular Ocean Model version 4.1 with vertical pressure layers, whereas ESM2G uses generalized ocean layer dynamics with a bulk mixed layer and interior isopycnal layers. On land, both ESMs include a revised land model to simulate competitive vegetation distributions and functioning, including carbon cycling among vegetation, soil, and atmosphere. In the ocean, both models include new biogeochemical algorithms including phytoplankton functional group dynamics with flexible stoichiometry. Preindustrial simulations are spun up to give stable, realistic carbon cycle means and variability. Significant differences in simulation characteristics of these two models are described. Because of differences in oceanic ventilation rates, ESM2M has a stronger biological carbon pump but weaker northward implied atmospheric CO 2 transport than ESM2G. The major advantages of ESM2G over ESM2M are improved representation of surface chlorophyll in the Atlantic and Indian Oceans and thermocline nutrients and oxygen in the North Pacific. Improved tree mortality parameters in ESM2G produced more realistic carbon accumulation in vegetation pools. The major advantages of ESM2M over ESM2G are reduced nutrient and oxygen biases in the southern and tropical oceans.

We document the configuration and emergent simulation features from the Geophysical Fluid Dynamics Laboratory (GFDL) OM4.0 ocean/sea ice model. OM4 serves as the ocean/sea ice component for the GFDL climate and Earth system models. It is also used for climate science research and is contributing to the Coupled Model Intercomparison Project version 6 Ocean Model Intercomparison Project. The ocean component of OM4 uses version 6 of the Modular Ocean Model and the sea ice component uses version 2 of the Sea Ice Simulator, which have identical horizontal grid layouts (Arakawa C‐grid). We follow the Coordinated Ocean‐sea ice Reference Experiments protocol to assess simulation quality across a broad suite of climate‐relevant features. We present results from two versions differing by horizontal grid spacing and physical parameterizations: OM4p5 has nominal 0.5° spacing and includes mesoscale eddy parameterizations and OM4p25 has nominal 0.25° spacing with no mesoscale eddy parameterization. Modular Ocean Model version 6 makes use of a vertical Lagrangian‐remap algorithm that enables general vertical coordinates. We show that use of a hybrid depth‐isopycnal coordinate reduces the middepth ocean warming drift commonly found in pure z* vertical coordinate ocean models. To test the need for the mesoscale eddy parameterization used in OM4p5, we examine the results from a simulation that removes the eddy parameterization. The water mass structure and model drift are physically degraded relative to OM4p5, thus supporting the key role for a mesoscale closure at this resolution.

[1] A three-dimensional oceanic state is estimated for the period 1992-1997 as it results from combining large-scale ocean data sets with a general circulation model. At the cost of increased computational load, the estimation (assimilation) method is chosen specifically so that the resulting state estimate is consistent with the model equations, having no artificial sources or sinks. To bring the model into close agreement with observations, its initial temperature and salinity conditions are permitted to change, as are the time-dependent surface fluxes of momentum, heat and freshwater. Resulting changes of these ''control vectors'' are largely consistent with accepted uncertainties in the hydrographic climatology and meteorological analyses. The assimilation procedure is able to correct for many of the traditional shortcomings of the flow field by changing the surface boundary conditions. Changes in the resulting flow field are predominantly on the gyre scale and affect many features that are often poorly simulated in traditional numerical simulations, such as the strengths of the Gulf Stream and its extension, the Azores Current and the anticyclonic circulation associated with the Labrador Sea. Tests of the results and their consistency with prior error assumptions show that the constrained model has moved considerably closer to the observations imposed as constraints, but has also moved closer to independent data from the World Ocean Circulation Experiment not used in the assimilation procedure. In some regions where the comparisons remain indeterminate, not enough ocean observations are available, and it is difficult to ascribe the residuals to either the model or the observations. Although problems remain, a useful first solution to the global time-dependent ocean state estimation problem has been found. The estimates will continue to improve through the evolution of numerical models, computer power increases, more data, and more efficient estimation methods.